Color image histogram equalization by absolute discounting back-off

Image enhancement aims at improving images from the human visual perspective. Image features such as edges, boundaries, and contrast are sharpened in a way that their dynamic range is increased without any change in the information content inherent in the data [1]. For this purpose, several techniques have been developed. Among others are contrast manipulation, noise reduction, edge crispening and sharpening, filtering, pseudocoloring, image interpolation and magnification [1].

Contrast manipulation techniques can be classified as either global or adaptive. Global techniques apply a transformation to all image pixels, while adaptive techniques use an input–output transformation that varies adaptively with the local image characteristics. The more common global techniques are linear contrast stretch, histogram equalization, and multichannel filtering. The most common adaptive techniques are adaptive histogram equalization (AHE) and contrast-limited adaptive histogram equalization (CLAHE) [2], [3]. AHE applies varying gray-scale transformations locally to every small image region, thus requiring the determination of the region size. CLAHE improves the just described technique by limiting the local contrast-gain. Two drawbacks of the latter method have been identified namely the unavoidable enhancement of noise in smooth regions and the image-dependent selection of the contrast-gain limit [4].

This paper is focused on global techniques with emphasis to color images. More precisely, the notion of unigram and bigram probabilities together with probability smoothing, borrowed from statistical language modeling, is applied to color histogram equalization in order to jointly equalize the two components of the HSI color space, namely the saturation and the intensity. The histogram equalization approach is partially built on that proposed in Pitas and Kiniklis [5], but it is extended with smoothing the necessary probabilities in order to counteract the effect of unseen color component combinations, which stems from the dimensionality of the color space and the often limited number of colors present in an image. Additionally, a second method is developed in an effort to eliminate the gamut problem by exploiting the transformations proposed in Naik and Murthy [6]. The performance of the proposed methods is compared to that of the methods proposed by Pitas and Kiniklis [5], [7] as well as the separate equalization of each color component. The comparison is conducted using not only subjective measures (i.e., how visually appealing the equalized images are), but also objective figures of merit, such as the entropy and the Kullback–Leibler divergence between the resulted color histogram and the corresponding multivariate uniform probability density function.

The outline of the paper is as follows. In Section 2, the color image histogram equalization methods are briefly presented. In Section 3, the baseline histogram equalization approaches and the novel algorithms, proposed in this paper, are described. Experimental results are demonstrated in Section 4, and finally, conclusions are drawn in Section 5. A brief description of the RGB and HSI color spaces is given in Appendix A.